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Unexplored Steiner Ratios in Geometric Networks

  • Paz Carmi
  • Lilach Chaitman-Yerushalmi
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7434)

Abstract

In this paper we extend the context of Steiner ratio and examine the influence of Steiner points on the weight of a graph in two generalizations of the Euclidean minimum weight connected graph (MST). The studied generalizations are with respect to the weight function and the connectivity condition.

First, we consider the Steiner ratio of Euclidean minimum weight connected graph under the budget allocation model. The budget allocation model is a geometric version of a new model for weighted graphs introduced by Ben-Moshe et al. in [4].

It is known that adding auxiliary points, called Steiner points, to the initial point set may result in a lighter Euclidean minimum spanning tree. We show that this behavior changes under the budget allocation model. Apparently, Steiner points are not helpful in weight reduction of the geometric minimum spanning trees under the budget allocation model (BMST), as opposed to the traditional model.

An interesting relation between the BMST and the Euclidean square root metric reveals a somewhat surprising result: Steiner points are also redundant in weight reduction of the minimum spanning tree in the Euclidean square root metric.

Finally, we consider the Steiner ratio of geometric t-spanners. We show that the influence of Steiner points on reducing the weight of Euclidean spanner networks goes much further than what is known for trees.

Keywords

Span Tree Minimum Span Tree Steiner Point Budget Allocation Steiner Tree Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Paz Carmi
    • 1
  • Lilach Chaitman-Yerushalmi
    • 1
  1. 1.Department of Computer ScienceBen-Gurion University of the NegevIsrael

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